Method/Codes

Non-Equilibrium Phase Search (NEPS) method

The Non-Equilibrium Phase Search method is designed to help elucidate the hysteresis and non-equilibrium reaction pathways associated with these conversion materials. We apply this methodology to investigate a variety of lithiation reaction pathways of Co3O4, NiO, MoS2, CuS, (Cu,Co)3O 4 by systematically exploring the energetics of a large number of equilibrium and non-equilibrium structural configurations using first-principle calculations.

The NEPS computational method involves, the following five steps, described below:

i) Starting with the host compound (which may or may not contain Li), identify all possible insertion sites. The method is initiated by searching for interstitial sites in the original transition metal oxide structures. An in-house code MINT (openly available on GitHub) was used which automates the search for insertion sites. The algorithm works by placing an analytic, exponential decaying function (Exp[-r/a]) at each atomic site and searching for geometric minima in the resulting function.

ii) Generate all symmetrically distinct configurations for Li insertion. We worked with the Enum code to generate all symmetrically-distinct configurations of Li on the unoccupied sites. All configurations were classified according to their composition Lix▢1-xMO.

iii) Compute total energies of all configurations generated in step ii). To enable a fast energy sampling, simple point-charge electrostatic calculations were usually conducted, using nominal charge states for the ions in the system. Alternatively, coarse DFT calculation can be performed to fulfill the energy sampling.

iv) Select the structures with lowest electrostatic energies to be computed more accurately and atomically-relaxed in DFT. For each composition, the structures were ranked by the electrostatic energies, and the three lowest energy structures were further relaxed using DFT. The formation energies for these selected structures were evaluated according to the following reaction: MO + xLi+ → LixMO.

v) Using all of these non-equilibrium structures derived from insertion of Li into the initial TM oxide, build the “non-equilibrium convex hull” and determine phases. For each specific system (Li-MO), we build the corresponding non-equilibrium convex hulls with the calculated formation energies at all compositions. The compositions, structures, energies located on the convex hull correspond to the identified non-equilibrium phases.

Here is an illustration of the NEPS method: Electrochemical lithiation process of Co3O4: